Related papers: Conformal four-point ladder integrals in diverse d…
In this thesis we propose a novel method to compute higher-order corrections to physical cross sections, bypassing more traditional approaches. This technique, the Four-Dimensional Unsubtraction (FDU), is based on the Loop-Tree Duality…
Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we…
We use the conformal group to study non-local operators in conformal field theories. A plane or a sphere (of any dimension) is mapped to itself by some subgroup of the conformal group, hence operators confined to that submanifold may be…
We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that…
We formulate the conformal bootstrap approach to four--fermion theory at its strong coupling fixed point in dimensions $2<d<4$. We present a solution of the bootstrap equations in the five--vertex approximation. We show that the bootstrap…
We consider four-point integrals arising in the planar limit of the conformal "fishnet" theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
We study multi-loop conformal integrals for four-point correlators of planar ${\cal N}=4$ super-Yang-Mills theory, and in particular those contributing to Coulomb branch amplitudes in the ten-dimensional lightlike limit, where linear…
We apply an integral transformation to solutions of a partial differential equation for five-point correlation functions in Liouville theory on a sphere with one degenerate field $V_{-\frac{1}{2b}}$. By repeating this transformation, we can…
We study logarithmic conformal field theory (LogCFT) in four dimensions using conformal bootstrap techniques in the large spin limit. We focus on the constraints imposed by conformal symmetry on the four point function of certain…
The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator…
We present the interpolating conformal algebra between the instant form dynamics (IFD) and the light-front dynamics (LFD) in $(1+1)$ dimensions, along with a $4\times4$ interpolating projective spacetime matrix representation. While there…
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…
We discuss specific hypergeometric solutions of the conformal Ward identities (CWI's) of scalar 4-point functions of primary fields in momentum space, in $d$ spacetime dimensions. We determine such solutions using various dual conformal…
Lorentzian 4-metrics are expressed in spinorial coordinates. In these coordinates the metric components can be factorized into a product of complex conjugate quantities. The linearized theory and Einstein's vacuum field equations are…
In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the $S^{D-1}$ spatial slice in radial quantization in $D=2,3$ dimensions. In each case, we use the conformal Ward Identities to solve…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…